Answer: ![(-9, 16]](https://tex.z-dn.net/?f=%28-9%2C%2016%5D)
This is the interval from -9 to 16. Exclude -9 but include 16.
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Work Shown:
The idea is to multiply all sides by 5, then add 1 to all sides
![-2 < x \le 3](https://tex.z-dn.net/?f=-2%20%3C%20x%20%5Cle%203)
![5(-2) < 5x \le 5(3)](https://tex.z-dn.net/?f=5%28-2%29%20%3C%205x%20%5Cle%205%283%29)
![-10 < 5x \le 15](https://tex.z-dn.net/?f=-10%20%3C%205x%20%5Cle%2015)
![-10+1 < 5x+1 \le 15+1](https://tex.z-dn.net/?f=-10%2B1%20%3C%205x%2B1%20%5Cle%2015%2B1)
![-9 < 5x+1 \le 16](https://tex.z-dn.net/?f=-9%20%3C%205x%2B1%20%5Cle%2016)
This converts to the interval notation ![(-9, 16]](https://tex.z-dn.net/?f=%28-9%2C%2016%5D)
note: a curved parenthesis means "do not include this value in the solution set"; while a square bracket has us include the value. So we exclude -9 and include 16.
Answer:
Range of Function : { - 9, - 5, - 1, 4 }
Step-by-step explanation:
We know that y = 2x - 5 provided the domain ( x - values ) { - 2, 0, 2, 4 }. Let us substitute each element in this set of domain as x in the equation "y = 2x - 5" as to solve for the y - values, otherwise known as the range of the function.
{ - 2, 0, 2, 4 }
y = 2( - 2 ) - 5 = - 9,
y = 2( 0 ) - 5 = - 5,
y = 2( 2 ) - 5 = - 1,
y = 2( 4 ) - 5 = 4
We have the set of y - values as { - 9, - 5, - 1, 4 }. This is the range of our function.
There are 3 in. of snow on the ground when it begins to snow 0.5 in./h.
Initial depth of snow = 3 in.
it begins to snow 0.5 in./h. The constant rate of snow is 0.5. So slope = 0.5
Let x be the number of hours
y be the total depth of the snow
To frame linear equation we use y=mx+b
where m is the slope and b is the y intercept (initial depth of snow)
We know m=0.5 and b=3
Replace it in the equation
y = 0.5x + 3
The linear equation that represents the total depth of the snow(y), in inches, after x hours
is y= 0.5x + 3